With regard to a normal running mode (engine brake running mode) performed with engine brake applied by driven rotation of an engine while power transmission between the engine and drive wheels is coupled, an inertia running mode performed with an engine brake force made lower than that of the normal running mode is conceived for extending a running distance and improving fuel consumption of a vehicle. A device described in Patent Document 1 is an example thereof and, if it is determined that an accelerator pedal returning operation is performed during running of a vehicle, a clutch disposed in a power transmission path between an engine and drive wheels is released to start the inertia running mode, thereby improving vehicle fuel consumption. The inertia running mode performed in Patent Document 1 has no distinction between an inertia running mode performed with a clutch released while engine rotation is stopped and an inertia running mode performed while an engine is kept rotating.